Gauge fields of the matrix Dirac equation

We introduce an equation named matrix Dirac equation which can be considered as a generalization of Dirac equation for an electron. The liaison between matrix Dirac equation and standard Dirac equation is discussed. We write a lagrangian from which matrix Dirac equation can be derived. This lagrangian is invariant under global unitary transformations of variables. The requirement of a local (gauge) invariance of lagrangian leads us to lagrangian with gauge fields.

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